因式分解 2x^2-4x+xy-y-6y^2+2

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因式分解 2x^2-4x+xy-y-6y^2+2
因式分解 2x^2-4x+xy-y-6y^2+2

因式分解 2x^2-4x+xy-y-6y^2+2
2x" - 4x + xy - y - 6y" + 2
= (2x" + xy - 6y") - 4x - y + 2
= (2x" + 4xy - 3xy - 6y") - 4x - y + 2
= [ 2x(x + 2y) - 3y(x + 2y) ] - 2x - 2x - 4y + 3y + 2
= (x + 2y)(2x - 3y) - 2x - 4y - 2x + 3y + 2
= (x + 2y)(2x - 3y) - 2(x + 2y) - (2x - 3y - 2)
= (x + 2y)(2x - 3y - 2) - (2x - 3y - 2)
= (x + 2y - 1)(2x - 3y - 2)

2x²-4x+xy-y-6y²+2=2x²+xy-6y²-4x-y+2=(2x-3y)(x+2y)-4x-y+2=(2x-3y-2)(x+2y-1)
双十字相乘法

(2x-3y)(x 2y)-(4x y)-2

(x 2y-1)(2x-3y-2)